Temperature and field stable relaxor-pt piezoelectric single crystals

ABSTRACT

The application is directed to piezoelectric single crystals having shear piezoelectric coefficients with enhanced temperature and/or electric field stability. These piezoelectric single crystal may be used, among other things, for vibration sensors as well as low frequency, compact sonar transducers with improved and/or enhanced performance.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of, and is a divisional applicationof co-pending U.S. patent application Ser. No. 13/206,971, now allowed,entitled “TEMPERATURE AND FIELD STABLE RELAXOR-PT PIEZOELECTRIC SINGLECRYSTALS”, and filed Aug. 10, 2011, which claims priority to and thebenefit of U.S. Provisional Application No. 61/372,439, filed Aug. 10,2010, both of which are hereby incorporated by reference in theirentirety.

STATEMENT OF FEDERALLY SPONSORED RESEARCH

Portions of the invention disclosed herein were reduced to practice withthe support of the U.S. Office of Naval Research, Contract No.N00014-07-C-0858. The U.S. Government may have certain rights in thisinvention.

FIELD

The present invention is generally directed to ferroelectric materials,and more particularly to relaxor-PT based piezoelectric single crystals.

BACKGROUND

For the past 50 years, perovskite Pb(Zr_(x)Ti_(1-x))O₃ (PZT)piezoelectric ceramics have dominated the commercial market ofelectronic devices, including piezoelectric sensors, actuators andmedical ultrasonic transducers, due to their high piezoelectric andelectromechanical coupling factors. For example, the shear piezoelectriccoefficient d₁₅ and electromechanical coupling factor k₁₅ for PZT5A type(DOD Type II) materials are found to be on the order of about 400 pC/Nand approximately 70%, respectively. Innovations in electronic deviceshave been the driving force for new developments in piezoelectricmaterials, including relaxor-PT single crystals.

The excellent piezoelectric properties of relaxor-PT single crystals,including Pb(Mg_(1/3)Nb_(2/3))O₃—PbTiO₃ (“PMN-PT”) andPb(In_(0.5)Nb_(0.5))O₃—Pb(Mg_(1/3)Nb_(2/3))O₃—PbTiO₃ (“PIN-PMN-PT”),have attracted considerable interest over the last decade, particularlyfor applications in high performance medical transducers. However, theircommercial use has been limited due to high variation of the dielectricand piezoelectric properties with temperature. Furthermore, the lowcoercive field of current relaxor-PT crystals further limits theirapplication.

Single crystal compositions near their respective morphotropic phaseboundaries (MPB) exhibit longitudinal piezoelectric coefficients (d₃₃)greater than 1500 pC/N with electromechanical coupling factors higherthan 90% along the pseudo-cubic <001> directions. These excellentproperties make relaxor-PT single crystals promising candidates forbroadband and high sensitivity ultrasonic transducers, sensors and otherelectromechanical devices. Specifically, certain applications of sensorsand transducers, such as accelerometers, vector sensors andnon-destructive evaluation (NDE) transducers, require large shearcoefficients d₁₅.

It has been reported that rhombohedral single domain PMN-PT crystalspoled along their spontaneous polarization direction [111], which may bereferred to as having the engineered domain configuration ‘1R’, where‘1’ represents a single domain crystal and ‘R’ represents therhombohedral phase, possess high shear values. For these materials,piezoelectric coefficients, d₁₅, and shear coupling factors, k₁₅, arereported to be >2000 pC/N and >90%, respectively, due to thepolarization rotation facilitated by the single domain state.Unfortunately, shear piezoelectric coefficients are found to increasesignificantly with increasing temperature, with more than a 200% changefrom room temperature to their respective ferroelectric phase transitiontemperatures. Hence, this strong temperature dependence severely limitstheir implementation in many electromechanical devices. Furthermore,relaxor-PT single crystals exhibit coercive fields on the order of <2-5kV/cm, thus limiting applications requiring large AC fields, such as NDEtransducers and high power sonar.

What is needed is a piezoelectric single crystal that does not sufferfrom one or more of the above drawbacks.

SUMMARY

According to certain exemplary embodiments, problems with knownrelaxor-PT single crystals are overcome by providing crystals having alarge shear piezoelectric coefficient d₂₄ achieved throughmonoclinic/orthorhombic relaxor-PT single crystals with ‘1O’ singledomain configuration. Such crystals have been found to possess nearlytemperature independent behavior over the temperature range of −50° C.to the orthorhombic to tetragonal phase transition temperature,generally on the order of about 75° C. to about 105° C.

Tetragonal and/or doped relaxor-PT crystals were found to possess highcoercive fields and/or internal bias fields while keeping very highshear piezoelectric coefficients comparable to the values of singledomain rhombohedral relaxor-PT crystals, providing crystals that can bedriven in shear under a high AC field.

Single crystals with ‘2R’ or ‘1O’ domain configuration and/or dopedrelaxor-PT crystals were also found to possess zero thickness shearpiezoelectric coefficients d₁₆ while keeping very high shearpiezoelectric coefficients d₁₅ comparable to the values of ‘1R’ singledomain rhombohedral relaxor-PT crystals.

Rotation of face (contour) shear d₃₆ single crystals with ‘2R’ domainconfiguration and/or relaxor-PT crystals around the crystallographicaxes were found to eliminate or minimize one of the transverse widthextensional piezoelectric coefficients.

The high shear piezoelectric properties of relaxor-PT single crystalswith new engineered domain configurations in accordance with exemplaryembodiments disclosed herein are promising for various electromechanicaldevice applications, such as vector sensors, non-destructive evaluation(NDE) transducers and low frequency sonar transducers, to name a few.

According to an exemplary embodiment, a piezoelectric single crystal hasa composition of the formula (1-x)Pb(Mg_(1/3)Nb_(2/3))O₃-xPbTiO₃(“PMN-xPT”) or yPb(In_(1/2)Nb_(1/2))O₃-(1-y-z)Pb(Mg_(1/3)Nb_(2/3))O₃-zPbTiO₃ (“yPIN-(1-y-z)PMN-zPT”), where0.305≦x≦0.355, 0.26<y≦0.50, 0.31<z≦0.36. The crystal is poled along thecrystallographic [110] direction and has an orthorhombic/monoclinicphase and ‘1O’ single domain state.

According to another exemplary embodiment, a piezoelectric singlecrystal has the formula PMN-xPT or yPIN-(1-y-z)PMN-zPT, where0.20<x≦0.305, 0.26<y≦0.50, 0.20<z≦0.31. The crystal is poled along thecrystallographic [110] direction and has a rhombohedral phase, a ‘2R’engineered domain configuration and macroscopic mm2 symmetry.

According to another exemplary embodiment, a piezoelectric singlecrystal has the formula PMN-xPT or yPIN-(1-y-z)PMN-zPT, where x>0.355,0.26<y≦0.50, z>0.36. The crystal is poled along the crystallographic[001] direction and has a ‘1T’ single domain state and macroscopic 4 mmsymmetry.

According to another exemplary embodiment, a ternary piezoelectricsingle crystal PIN-PMN-PT with rhombohedral phase is provided whereinthe crystal is poled along the crystallographic [111] direction androtated to provide a shear piezoelectric coefficient d₁₆ that is lessthan about 100 pC/N.

An advantage of exemplary embodiments is that a piezoelectric singlecrystal is provided having shear piezoelectric coefficients withtemperature stability.

Another advantage of exemplary embodiments is that a piezoelectricsingle crystal is provided with improved AC field drive stability.

Still another advantage of exemplary embodiments is that piezoelectricsingle crystals are provided having shear piezoelectric coefficientsthat are more stable in temperature and/or electric field thanpreviously known single crystals. Such single crystals in accordancewith exemplary embodiments may be used, for example, as vibrationsensors as well as low frequency, compact sonar transducers withimproved and/or enhanced performance.

Other features and advantages will be apparent from the following moredetailed description of exemplary embodiments, taken in conjunction withthe accompanying drawings which illustrate, by way of example, theprinciples of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic phase diagram for relaxor-PT based crystals, whereR, O and T represent rhombohedral, orthorhombic/monoclinic andtetragonal phase regions.

FIG. 2 is a schematic of various shear mode samples.

FIG. 3 shows two independent shear piezoelectric modes (15- and 24-) andrelated polarization rotation paths in orthorhombic crystals.

FIG. 4 shows the temperature dependence of shear piezoelectriccoefficients for orthorhombic relaxor-PT based single crystals.

FIG. 5( a) shows the polarization hysteresis for pure d₁₅ [110]/(−110)PIN-PMN-PT crystals with ‘2R’ engineered domain configuration.

FIG. 5( b) shows the polarization loops for the first and 5000th cyclesat different electric field drive levels for pure d₁₅ [110]/(−110)PIN-PMN-PT crystals with ‘2R’ engineered domain configuration.

FIG. 5( c) shows the impedance characteristics for shear thicknessvibration mode after cycles at different levels for pure d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘2R’ engineered domainconfiguration.

FIG. 6( a) shows the polarization hysteresis for manganese doped d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘2R’ engineered domainconfiguration.

FIG. 6( b) shows the polarization loops for the first and 5000th cyclesat different electric field drive levels for manganese doped d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘2R’ engineered domainconfiguration.

FIG. 6( c) shows the impedance characteristics for shear thicknessvibration mode after cycles at different levels for manganese doped d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘2R’ engineered domainconfiguration.

FIG. 7( a) shows the polarization hysteresis for pure d₁₅ [110]/(−110)PIN-PMN-PT crystals with ‘1O’ engineered domain configuration.

FIG. 7( b) shows polarization loops for the first and 5000th cycles atdifferent electric field drive levels for pure d₁₅ [110]/(−110)PIN-PMN-PT crystals with ‘1O’ engineered domain configuration.

FIG. 7( c) shows impedance characteristics for shear thickness vibrationmode after cycles at different levels for pure d₁₅ [110]/(−110)PIN-PMN-PT crystals with ‘1O’ engineered domain configuration.

FIG. 8( a) shows polarization hysteresis for manganese doped d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘1O’ engineered domainconfiguration.

FIG. 8( b) shows polarization loops for the first and 5000th cycles atdifferent electric field drive levels for manganese doped d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘1O’ engineered domainconfiguration.

FIG. 8( c) shows impedance characteristics for shear thickness vibrationmode after cycles at different levels for manganese doped d₁₅[110]/(−110) PIN-PMN-PT crystals with ‘1O’ engineered domainconfiguration.

FIG. 9( a) shows polarization hysteresis for pure [001]/(100) PIN-PMN-PTcrystals with ‘1T’ engineered domain configuration.

FIG. 9( b) shows polarization loops for the first and 5000th cycles atdifferent electric field drive levels for pure [001]/(100) PIN-PMN-PTcrystals with ‘1T’ engineered domain configuration.

FIG. 9( c) shows impedance characteristics for shear thickness vibrationmode after cycles at different levels for pure [001]/(100) PIN-PMN-PTcrystals with ‘1T’ engineered domain configuration.

FIG. 10( a) shows polarization hysteresis for manganese doped[001]/(100) PIN-PMN-PT crystals with ‘1T’ engineered domainconfiguration.

FIG. 10( b) shows polarization loops for the first and 5000th cycles atdifferent electric field drive levels for manganese doped [001]/(100)PIN-PMN-PT crystals with ‘1T’ engineered domain configuration.

FIG. 10( c) shows impedance characteristics for shear thicknessvibration mode after cycles at different levels for manganese doped[001]/(100) PIN-PMN-PT crystals with ‘1T’ engineered domainconfiguration.

FIG. 11( a) shows polarization hysteresis for manganese doped[001]/(110) PIN-PMN-PT crystals with ‘1T’ engineered domainconfiguration.

FIG. 11( b) shows polarization loops for the first and 5000th cycles atdifferent electric field drive levels for manganese doped [001]/(110)PIN-PMN-PT crystals with ‘1T’ engineered domain configuration.

FIG. 11( c) shows impedance characteristics for shear thicknessvibration mode after cycles at different levels for manganese doped d₁₅[001]/(110) PIN-PMN-PT crystals with ‘1T’ engineered domainconfiguration.

FIG. 12( a) shows the polarization hysteresis for pure d₁₅ [111]/(1-10)PIN-PMN-PT crystals with ‘1R’ engineered domain configuration.

FIG. 12( b) shows the polarization loops for the first and 5000th cyclesat different electric field drive levels for pure d₁₅ [111]/(1-10)PIN-PMN-PT crystals with ‘1R’ engineered domain configuration.

FIG. 12( c) shows the impedance characteristics for shear thicknessvibration mode after cycles at different levels for pure d₁₅[111]/(1-10) PIN-PMN-PT crystals with ‘1R’ engineered domainconfiguration.

FIG. 13( a) shows the polarization hysteresis for manganese doped d₁₅[111]/(1-10) PIN-PMN-PT crystals with ‘1R’ engineered domainconfiguration.

FIG. 13( b) shows the polarization loops for the first and 5000th cyclesat different electric field drive levels for manganese doped d₁₅[111]/(1-10) PIN-PMN-PT crystals with ‘1R’ engineered domainconfiguration.

FIG. 13( c) shows the impedance characteristics for shear thicknessvibration mode after cycles at different levels for manganese doped d₁₅[111]/(1-10) PIN-PMN-PT crystals with ‘1R’ engineered domainconfiguration.

FIG. 14 shows rotation about the X axis to reduce or eliminate the d₁₆coefficient while maintaining polarization in the <111> axis for d₁₅[111]/(1-10) PIN-PMN-PT crystals with ‘1R’ engineered domainconfiguration.

FIG. 15 the measured d₁₅ and d₁₆ shear piezoelectric coefficients ford₁₅ [111]/(1-10) PIN-PMN-PT crystals with ‘1R’ domain configurationrotated about the X axis at angles from −26° to +26°.

FIG. 16 shows the measured d₁₅ and d₁₆ shear strain field curves for[110]/(−110) PMN-PT crystal with ‘2R’ engineered domain configuration

FIG. 17 shows the measured d₁₅ and d₁₆ shear strain field curves for d₁₅[110]/(−110) PIN-PMN-PT crystal with ‘2R’ engineered domainconfiguration.

FIG. 18 shows the measured d₁₅ and d₁₆ shear strain field curves for d₁₅manganese modified [110]/(−110) PIN-PMN-PT crystal stack of three bondedplates with ‘2R’ engineered domain configuration.

FIG. 19 shows a d₃₆ face shear [110]/(110) single crystal with ‘2R’engineered domain configuration and a rotated angle theta thateliminates one of the transverse width extensional piezoelectriccoefficients d₃₁′ or d₃₂′.

FIG. 20 shows the measured d₃₁′ and d₃₂′ strain field curves for a d₃₆face shear [110]/(110) PMN-PT single crystal with ‘2R’ engineered domainconfiguration, showing near elimination of the d₃₂′.

It will be appreciated that in figures showing more than one line on agraph, identifiers are used to aid in differentiation, although thespecific location of an identifier along the line is not necessarilyintended to correspond to any particular data point.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Exemplary embodiments provide for composition ranges andcrystallographic orientations of piezoelectric single crystals where theshear piezoelectric coefficients are more stable in temperature and/orelectric field. The disclosed piezoelectric single crystals may be used,for example, as vibration sensors and low frequency, compact sonartransducers with improved and/or enhanced performance.

It has been discovered that composition ranges and crystal cuts inaccordance with exemplary embodiments give rise to certain crystalstructures with increased shear coefficients. It has further beendiscovered that these crystal structures, composition ranges, andcrystal cuts result in an unexpected improvement in shear propertystability.

It has also been discovered that composition ranges and crystal cuts inaccordance with exemplary embodiments give rise to certain crystalstructures with eliminated or minimized transverse shear coefficients orwidth extensional coefficients.

Accordingly, exemplary embodiments are directed to composition ranges,crystal structures, and properties described herein that have high sheartemperature stability and/or AC field stability. As used herein, theletters R, O and T refer to a domain state having a rhombohedral,orthorhombic/monoclinic, or tetragonal phase, respectively, while aleading number in front of that letter refers to the number of domainspresent, which may be a single domain (i.e., a leading 1) ormulti-domain (e.g., a leading 2, 3 or 4).

Generally, embodiments relate to a piezoelectric single crystal having acomposition with the formula (1-x)Pb(Mg_(1/3)Nb_(2/3))O₃-xPbTiO₃(“PMN-xPT”) or yPb(In_(1/2)Nb_(1/2))O₃-(1-y-z)Pb(Mg_(1/3)Nb_(2/3))O₃-zPbTiO₃ (“yPIN-(1-y-z)PMN-zPT”), where x>0.2,0.26≦y≦0.50, and z>0.2, the crystal having a multi-domain rhombohedral,single-domain orthorhombic/monoclinic or tetragonal phase and a finitepiezoelectric shear coefficient or to a piezoelectric single crystalhaving a composition with the formula yPIN-(1-y-z)PMN-zPT, where0.26≦y≦0.50, z>0.2, the crystal having a single-domain rhombohedralphase and a finite piezoelectric shear coefficient.

In one embodiment, a piezoelectric single crystal has a composition ofthe formula PMN-xPT or yPIN-(1-y-z)PMN-zPT, where 0.305<x≦0.355,0.26≦y≦0.50, 0.31<z≦0.36. The crystal has an orthorhombic/monoclinicphase. The crystal is poled along the crystallographic [110] directionand has a ‘1O’ single domain state. The crystal exhibitstemperature-stable piezoelectric shear properties.

In a further embodiment, x=0.32, y=0.26, z=0.33 and the crystal hasmacroscopic mm2 symmetry. In some embodiments, with electrodes on the(001) faces of the crystal, the crystal has a shear vibration with a k₂₄of about 85% and a shear piezoelectric coefficient d₂₄ of about2000pC/N. The shear piezoelectric coefficient d₂₄ is substantiallystable in temperature range of −50° C. to about T_(OT), where the T_(OT)is orthorhombic to tetragonal phase transition temperature.

In another embodiment having this composition but in which electrodesare on the (−110) faces, the crystal has a k₁₅ of about 90% and a shearpiezoelectric coefficient d₁₅ of about 3000 pC/N. In such cases, theshear mode properties of yPIN-(1-y-z)PMN-zPT shows particular improvedAC field stability under high drive. The coercive field is about 5 kV/cmfor pure (i.e., undoped) crystals, the allowable AC field drive level ofpure crystal is 40% of coercive fields, being on the order of about2kV/cm.

In another embodiment, the piezoelectric single crystal previouslydescribed is doped with between about 0.2 mol % and about 8 mol % of adopant selected from the group consisting of manganese, iron, cobalt,nickel, aluminum, gallium, copper, potassium sodium, fluorides andcombinations thereof. In one embodiment, the dopants are provided byintroducing one or more of the following compounds into the composition:MnO₂, MnCO₃, Fe₂O₃, Co₂O₃, CoCO₃, Ni₂O₃, NiCO₃, Al₂O₃, Ga₂O₃, Cu₂O, CuO,K₂CO₃, Na₂CO₃, fluoride and/or combinations thereof. Single crystalshaving such doped compositions also result in temperature stablepiezoelectric shear properties. Preferably, the dopant is present atabout 1 mol % to about 3 mol % and in some preferred embodiments, thedopant is manganese (introduced, e.g., by MnO₂ and/or MnCO₃). In oneembodiment, x=0.32, y=0.26, z=0.33 and the crystal is doped with about1.5 mol % manganese.

As with the pure orthorhombic/monoclinic crystal, the doped crystal maybe poled along the [110] crystallographic direction to achieve a ‘1O’single domain state with macroscopic mm2 symmetry. In an embodimenthaving this composition, the crystal has electrodes on the (001) faces,a k₂₄ of about 85% and a shear piezoelectric coefficient d₂₄ of about2000 pC/N. The shear piezoelectric coefficient d₂₄ was substantiallystable in the usage temperature range of −50° C. to about T_(OT).

In another embodiment this composition, the crystal may be poled alongthe [110] crystallographic direction and has electrodes on the (−110)faces, and has a k₁₅ of about 90% and a shear piezoelectric coefficientd₁₅ of about 3000 pC/N. The shear mode properties of yPIN-(1-y-z)PMN-zPTin particular showed improved AC field stability under high drive. Thecoercive field is further increased to about 7 to 9 kV/cm for such dopedcrystals, with internal bias field of about 1 kV/cm. The allowable ACfield drive level of the doped crystals is 60-70% of their respectivecoercive fields, being on the order of about 4 to 6 kV/cm, due to theinternal bias.

In one embodiment, a piezoelectric single crystal has a composition ofthe formula PMN-xPT or yPIN-(1-y-z)PMN-zPT, where x≧0.355, 0.26≦y≦0.50,z≧0.36, the crystal poled along the [001] direction. The crystal has atetragonal phase, having a ‘1T’ single domain state and macroscopic 4 mmsymmetry. In one embodiment, x=0.36, y=0.26, and z=0.37.

In one embodiment of the tetragonal crystal, electrodes are on the (100)and/or (110) faces, with a k₁₅ of about 75-85% and a d₁₅ of about1000-2500 pC/N. In such embodiments, the shear mode properties ofyPIN-(1-y-z)PMN-zPT crystals in particular has improved AC fieldstability under high drive. The coercive field is >11 kV/cm, with anallowable AC field drive level that is about 40% of coercive fields,being on the order of about 4-5kV/cm.

In another embodiment, the piezoelectric single crystal previouslydescribed is doped with between about 0.2 mol % and about 8 mol % of adopant selected from the group consisting of manganese, iron, cobalt,nickel, aluminum, gallium, copper, potassium sodium, fluorides andcombinations therefore. The dopants may be provided by introducing oneor more of the following compounds into the composition: MnO₂, MnCO₃,Fe₂O₃, Co₂O₃, CoCO₃, Ni₂O₃, NiCO₃, Al₂O₃, Ga₂O₃, Cu₂O, CuO, K₂CO₃,Na₂CO₃, fluoride and/or combinations thereof. Such single crystalshaving such doped compositions also result in temperature-stablepiezoelectric shear properties. Preferably, the dopant is present atbetween about 1 mol % and about 3 mol % and in some preferredembodiments, the dopant is manganese (introduced, e.g., by MnO₂ and/orMnCO₃). In one embodiment, x=0.36, y=0.26, and z=0.37 and the crystal isdoped with 1.5 mol % manganese.

In an embodiment where the doped tetragonal crystal has electrodes onthe (100) and/or (110) faces, k₁₅ of about 75-85% and d₁₅ of about1000-2500 pC/N, the shear mode properties of yPIN-(1-y-z)PMN-zPTcrystals in particular has improved AC field stability under high drive.The coercive field is >11 kV/cm for doped crystals, with internal biasfield of about 1-2 kV/cm. The allowable AC field drive level is betweenabout 60 and about 70% of their respective coercive fields, being on theorder of about 7-8kV/cm, due to the internal bias.

In yet another embodiment, a piezoelectric single crystal has acomposition of the formula PMN-xPT or yPIN-(1-y-z)PMN-zPT, where0.20≦x≦0.305, 0.26≦y≦0.50, 0.20≦z≦0.31. The crystal is in therhombohedral phase. The crystal is poled along the crystallographic<110> direction, has a ‘2R’ engineered domain configuration andmacroscopic mm2 symmetry.

In another embodiment having of this composition, the crystal is poledalong the crystallographic direction and electrodes on the (−110) faces.The crystal has no or minimal transverse piezoelectric coefficient d₁₆(i.e., the absolute value of d₁₆ is less than about 100 pC/N, preferablyless than about 50 pC/N).

In another embodiment having this composition, the crystal is poledalong the [110] crystallographic direction, has electrodes on the (110)faces, and the crystal is rotated around the Z-axis (i.e., the polingaxis, as will be appreciated by those of ordinary skill). The crystalhas a face shear component piezoelectric coefficient d₃₆ that isdependent on the transverse width extensional piezoelectric coefficientsd₃₁ and d₃₂ of the crystal before rotation. The crystal further exhibitsan elimination or reduction of the rotated transverse width extensionalpiezoelectric coefficients d₃₁′ or d₃₂′ (i.e., the absolute value of theminimized rotated transverse width extensional piezoelectric coefficientis less than or equal to about 50 pC/N, preferably less than about 25pC/N). When the d₃₁′ is eliminated/reduced, the crystal is rotatedaround the Z-axis by an angle:

$\theta_{31} = {\arctan \left( \sqrt{\frac{- d_{31}}{d_{32}}} \right)}$

When the d₃₂′ is eliminated/reduced, the crystal is rotated around theZ-axis by an angle:

$\theta_{32} = {\arctan \left( \sqrt{\frac{- d_{32}}{d_{31}}} \right)}$

In another embodiment having this composition, the electrodes are on the(−110) faces, with a k₁₅ of about 90%, a d₁₅ of about 2000 pC/N and ad₁₆ of about 50 pC/N in which shear mode properties ofyPIN-(1-y-z)PMN-zPT crystals in particular has improved AC fieldstability under high drive. The coercive field is about 5 kV/cm, withallowable AC field drive level about 40% of the coercive field, being onthe order of about 2kV/cm.

In another embodiment having this composition, the electrodes are on the(110) faces, with a d₃₂ of about 1270 pC/N, d₃₁ of about −460 pC/N and arotation around the Z-axis of about 31.5°. The d₃₆ is about 1540 pC/N,d₃₁′ is about 780 pC/N and d₃₂′ is about −20 pC/N.

In another embodiment, the piezoelectric single crystal previouslydescribed is doped with between about 0.2 mol % and about 8 mol % of adopant selected from the group consisting of manganese, iron, cobalt,nickel, aluminum, gallium, copper, potassium sodium, fluorides andcombinations therefore. The dopants may be provided by introducing oneor more of the following compounds into the composition: MnO₂, MnCO₃,Fe₂O₃, Co₂O₃, CoCO₃, Ni₂O₃, NiCO₃, Al₂O₃, Ga₂O₃, Cu₂O, CuO, K₂CO₃,Na₂CO₃, fluoride and/or combinations thereof. Single crystals havingsuch doped compositions also result in temperature stable piezoelectricshear properties. Preferably, the dopant is present at between about 1mol % and about 3 mol % and in some preferred embodiments, the dopant ismanganese (introduced, e.g., by MnO₂ and/or MnCO₃).

In one embodiment, x=0.29, y=0.26, z=0.29, and the crystal is doped withabout 1.5 mol %, manganese. In another embodiment, the crystal has avibration direction of [−110], a k_(is) of about 90% and a d₁₅ of about2000 pC/N; shear mode properties of yPIN-(1-y-z)PMN-zPT crystals inparticular has improved AC field stability under high drive. Thecoercive field is about 7 kV/cm to about 9 kV/cm for doped crystals,with internal bias field of about 1 kV/cm. The allowable AC field drivelevel increase to between about 60 and about 70% of the coercive field,due to the internal bias.

In one embodiment, the crystal is doped with 1.5 mol %, manganese. Inanother embodiment, the crystal has the electrodes on the (−110) faces,a k₁₅ of about 90%, a d₁₅ of about 2000 pC/N and a d₁₆ of about 0 pC/N;shear mode properties of yPIN-(1-y-z)PMN-zPT crystals in particular hasimproved AC field stability under high drive. The coercive field isabout 7 kV/cm to about 9 kV/cm for doped crystals, with internal biasfield of about 1 kV/cm. The allowable AC field drive level increase tobetween about 60 and about 70% of their respective coercive fields, dueto the internal bias.

In one embodiment, a piezoelectric single crystal has a composition ofthe formula yPIN-(1-y-z)PMN-zPT, where 0.26≦y≦0.50, 0.20≦z≦0.31. Thecrystal is poled along the [111] crystallographic direction, haselectrodes on the (1-10) faces and a ‘1R’ domain configuration. Thecrystal is rotated around the X-axis by an angle:

$\gamma = {\arctan \left( \frac{d_{16}}{d_{15}} \right)}$

The crystal exhibits a rotated transverse shear coefficient d₁₆ of zeroor some other minimal value (i.e., less than about 100 pC/N).

In another embodiment having this composition, the crystal is rotatedaround the X-axis by about 25° and has a d₁₅ of about 3300 pC/N and ad₁₆ of about 0 pC/N.

In another embodiment, the piezoelectric single crystal previouslydescribed is doped with between about 0.2 mol % and about 8 mol % of adopant selected from the group consisting of manganese, iron, cobalt,nickel, aluminum, gallium, copper, potassium sodium, fluorides andcombinations therefore. The dopants may be provided by introducing oneor more of the following compounds into the composition: MnO₂, MnCO₃,Fe₂O₃, Co₂O₃, CoCO₃, Ni₂O₃, NiCO₃, Al₂O₃, Ga₂O₃, Cu₂O, CuO, K₂CO₃,Na₂CO₃, fluoride and/or combinations thereof. Single crystals havingsuch doped compositions also result in temperature stable piezoelectricshear properties. Preferably, the dopant is present at between about 1mol % and about 3 mol % and in some preferred embodiments, the dopant ismanganese (introduced, e.g., by MnO₂ and/or MnCO₃).

The single crystals described herein can be manufactured according toany suitable techniques for crystal growth and thereafter cut using anysuitable cutting techniques to achieve the desired compositions andconformations.

FIG. 1 is a schematic phase diagram for relaxor-PT based crystals, whereR, O and T represent a rhombohedral phase region, anorthorhombic/monoclinic (M_(C)) phase region and a tetragonal phaseregion. The monoclinic (M_(C)) phase region of exemplary embodiments isa slightly distorted orthorhombic phase; thus, the M_(C) phase regionwas analyzed as a pseudo-orthorhombic phase. FIG. 2 shows a schematic ofvarious shear mode crystals, in which crystal A is [111]/(1-10); crystalB is [110]/(−110); crystal C is [110]/(001); crystal D is [001]/(110);and crystal E is [001]/(100).

According to one exemplary embodiment described herein, crystal C isprovided having a new crystal cut [110]/(001), where [110] refers to thepoling direction and (001) refers to the electrode orientation face, inrelaxor-PT crystals, compositionally lying in the monoclinic phase. Thecompositions for Crystal C possess a good ‘1O’ orthorhombic singledomain state after polarization along the [110] orientation. A shearpiezoelectric coefficient d₂₄ observed in such cases reflects comparableshear piezoelectric coefficients to d₁₅ in the ‘1R’ domain state, beingon the order of greater than about 2000 pC/N. The crystal C, [110]/(001)cut, exhibits good thermal stability over a wide temperature range ofabout −50° C. to about T_(OT) (orthorhombic to tetragonal phasetransition temperature). In another embodiment, tetragonal and/or dopedrelaxor-PT single crystals exhibit improved AC and DC driving-fieldstability under large signal measurements.

The temperature stability of shear piezoelectric coefficients (d₂₄ vsd₁₅ in ‘1O’ domain state) is now briefly discussed. Shear piezoelectricresponse is in direct proportion to the transverse dielectricpermittivity, spontaneous polarization and electrostrictive coefficient.Regardless of the occurrence of phase transitions, the variation ofspontaneous polarization and electrostrictive coefficient are quitesmall when compared to the dielectric permittivity. Thus, the change inpiezoelectric coefficient with temperature is mainly determined by thevariation of the dielectric permittivity. A facilitated polarizationrotation process corresponds to a ‘higher’ level of transversedielectric permittivity and shear piezoelectric coefficient.

Two independent shear piezoelectric coefficients d₁₅ and d₂₄ are presentfor the case of [110] poled orthorhombic crystals (mm2 symmetry). Asshown in FIG. 3, the polarization rotation paths of piezoelectric 15-and 24-modes are [110]_(C)→[100]_(C) and [110]_(C)→[111]_(C),respectively. FIG. 3 shows the two independent shear piezoelectric modes(15- and 24-) and related polarization rotation paths in orthorhombiccrystals, where the arrow 302 represents the spontaneous polarization.The principle axes are [−110], [001] and [110] directions. The arrow 304and the arrow 306 represent the [100] and [111] directions,respectively. The shear piezoelectric coefficient d₁₅ increases withtemperature and/or composition as either approach anorthorhombic-tetragonal (O-T) phase boundary. The coefficient d₂₄increases with temperature and/or composition as either approach anorthorhombic-rhombohedral (O-R) phase boundary. Thus, it can be foundthat the shear coefficient d₁₅ is not stable with respect to temperaturefor orthorhombic relaxor-PT based crystals, since the O-T phase boundarygenerally occurs above room temperature. In contrast to the O-T phasetransition, a nearly ‘vertical’ O-R phase boundary exists in the phasediagram of relaxor-PT single crystal systems, as shown in FIG. 1.Utilizing this “vertical” phase boundary, orthorhombic crystalcompositions can be selected near the O-R phase boundary in order toobtain high shear piezoelectric coefficients d₂₄, with temperatureindependent characteristic of d₂₄, since no O-R phase transition occursin the studied temperature range for orthorhombic/monoclinic crystals.

FIG. 4 shows the temperature dependence of shear piezoelectriccoefficients for orthorhombic PMN-xPT and yPIN-(1-y-z)PMN-zPT crystalswith x=0.32, y=0.26 and z=0.33. As can be seen in FIG. 4, d₂₄ has anearly temperature independent characteristic. For the orthorhombiccrystals, the piezoelectric coefficient d₂₄ is approximately 2100 pC/Nfor both PIN-PMN-PT and PMN-PT crystals at room temperature, maintainingsimilar values over the temperature range from −50° C. to theirrespective O-T phase transition temperatures, which are approximately80° C. for PMN-PT and 100° C. for PIN-PMN-PT. As previously noted,however, the coefficient d₁₅ of orthorhombic PIN-PMN-PT crystalsincreased from about 2300 pC/N to about 7000 pC/N with increasingtemperature from about −50° C. to about 100° C.

Embodiments of the present invention also result in improved AC fielddrive stability. The polarization electric field behavior for pure[110]/(−110) yPIN-(1-y-z)PMN-zPT crystals, with y=0.26 and z=0.29, witha ‘2R’ engineered domain configuration is shown in FIG. 5( a), fromwhich the coercive field EC is found to be on the order of about 5 kV/cmfor [−110] oriented samples. The polarization loops as a function ofcycling and electric field drive level are given in FIG. 5( b). Theimpedance characteristics for shear thickness vibration mode aftercycling measurements (5000 cycles) at different field levels are shownin FIG. 5( c). For an AC drive field of 2 kV/cm at a frequency of 10 Hz,the polarization versus electric field (PE) loops after 5000 cyclesshowed exactly the same linear behavior as the 1st cycle, indicating thesamples in the poled condition exhibited no domain reversal or fatigue.This demonstrated field stability was confirmed by theimpedance-frequency characteristics of shear vibrated samples, asobserved in FIG. 5( c), where no impedance changes with increasing fieldare observed. The PE loops become nonlinear with increasing the drivefield, showing hysteretic behavior. The remnant polarization was foundto increase significantly to of about 0.2 C/m² after 5000 cycles at adrive field of 3.5 kV/cm, demonstrating that samples were re-poled alongthe applied field direction [−110]. As a consequence, the shearvibration characteristic disappeared in the impedance frequency spectra;instead, a new lateral vibration mode observed in the lower frequencyrange, demonstrating that the samples were poled along [−110] directionwith vibration direction along [110]/[001].

FIG. 6 shows the ferroelectric and shear electromechanical propertiesfor 1.5 mol % manganese doped [110]/(−110) yPIN-(1-y-z)PMN-zPT crystalshaving the same y and z compositional ratios as discussed with respectto FIG. 5, with ‘2R’ engineered domain configuration, where thepolarization electric field behavior is shown in FIG. 6( a). Thepolarization electric field behavior as a function of cycling andelectric field drive level (as shown in FIG. 6( b)), with thecorresponding impedance characteristics for shear thickness vibrationmode after fatigue measurements at different levels are given in FIG. 6(c). For the doped crystals, the coercive field was found to be on theorder of approximately 7 kV/cm, with an identified internal bias fieldat 1.2 kV/cm, as shown in FIG. 6( a). Without wishing to be bound bytheory, it is believed the development of an internal bias is due toacceptor-oxygen vacancy defect dipoles in the crystals which move to thehigh-stressed areas of domain walls by diffusion, pin the domain walls,and stabilize the domains. The build-up of these parallel defect dipolesto the local polarization vector leads to an offset of P-E behavior orinternal bias. For an AC drive field at the level of 2-5 kV/cm at 10 Hzfrequency, the polarization versus electric field (PE) loops after 5000cycles exhibited the same linear behavior as the 1st cycle, indicatingthe manganese doped crystals still remain in the [110] poled conditionand that no domain reversal occurred. This field polarization stabilitycan be confirmed by the impedance-frequency characteristic of theshear-vibrated samples, as observed in FIG. 6( c). Further increasingthe AC drive field level to 6 kV/cm (near coercive field), the PE loopsare larger, showing hysteretic behavior. As a consequence, the shearvibration characteristic disappeared with a new lateral vibration modeappear in the impedance frequency spectra. Thus, the combination of ahigh coercive field and internal bias in manganese doped PIN-PMN-PTcrystals allowed a higher AC drive field level than pure crystals.

The ferroelectric and shear mode electromechanical properties for pureand manganese doped [110]/(−110) yPIN-(1-y-z)PMN-zPT crystals, withy=0.26 and z=0.33 and manganese about 1.5%, with ‘1O’ domainconfigurations are shown in FIG. 7 and FIG. 8, respectively. Asdiscussed for FIG. 5 and FIG. 6, the stability of AC drive field forpure PIN-PMN-PT crystals with ‘1O’ engineered domain configuration wasfound to be about 2 kV/cm, while being on the order of about 5 kV/cm forthe manganese doped crystals with the same domain configuration,attributable to the higher coercive field and internal bias field in thedoped crystals.

FIG. 9( a) and FIG. 10( a) give the polarization hysteresis for,respectively, pure and manganese doped [001]/(100) yPIN-(1-y-z)PMN-zPTtetragonal crystals with ‘1T’ domain configurations, with y=0.26 andz=0.37. In the doped crystals, manganese doping was about 1.5 mol %. Thepolarization loops as a function of cycling and electric field levelsare shown in FIGS. 9( b) & 10(b), with impedance characteristics forshear thickness vibration mode samples after fatigue cycling are shownin FIGS. 9( c) & 10(c), respectively. In contrast to the rhombohedraland/or monoclinic crystals, the tetragonal PIN-PMN-PT samples were foundto possess relatively high coercive field, being on the order of 11kV/cm, thus in favor of the large AC drive field, without any depolingand/or degradation of the shear mode properties until 4-5 kV/cm, whilemanganese doping further increased the drive field level to 6 kV/cm.

FIG. 11 shows the ferroelectric and shear mode electromechanicalproperties for the manganese doped [001]/(110) tetragonal PIN-PMN-PTcrystals with a ‘1T’ domain configuration discussed with respect to FIG.10( a)-(c). The polarization electric field behavior is given in FIG.11( a); polarization loops as a function of cycling and electric fielddrive levels are shown in FIG. 11( b), while impedance characteristicsfor the shear thickness vibration mode after fatigue/cyclingmeasurements at different levels are given in FIG. 11( c). The shearpiezoelectric properties are comparable to [001]/(100) crystals, butwith significantly higher allowable AC drive field, being on the orderof 8 kV/cm.

The polarization electric field behavior for pure [111]/(1-10)yPIN-(1-y-z)PMN-zPT crystals, with y=0.26 and z=0.29, with a ‘1R’ singledomain configuration is shown in FIG. 12( a), from which the coercivefield E_(C) is found to be on the order of about 4.5 kV/cm for [1-10]oriented samples. The polarization loops as a function of cycling andelectric field drive level are given in FIG. 12( b). The impedancecharacteristics for shear thickness vibration mode after cyclingmeasurements (5000 cycles) at different field levels are shown in FIG.12( c). For an AC drive field of 2 kV/cm at a frequency of 10 Hz, thepolarization versus electric field (PE) loops after 5000 cycles showedthe same linear behavior as the first cycle, indicating the samples inthe poled condition exhibited no domain reversal or fatigue at 2kV/cm.This demonstrated field stability was confirmed by theimpedance-frequency characteristics of shear vibrated samples, asobserved in FIG. 12( c), where no impedance changes with increasingfield are observed. The PE loops become nonlinear with increasing thedrive field, showing hysteretic behavior. The remnant polarization wasfound to increase to about 0.01 C/m² after 5000 cycles at a drive fieldof 3 kV/cm, where the impedance was observed to decrease at resonanceand antiresonance frequencies, indicating the safe AC drive field isabout 2kV/cm.

FIG. 13 shows the ferroelectric and shear electromechanical propertiesfor manganese doped [111]/(1-10) yPIN-(1-y-z)PMN-zPT crystals, withy=0.26 and z=0.29 and manganese about 1.5 mol %, with ‘1R’ engineereddomain configuration, where the polarization electric field behavior isshown in FIG. 13( a). As shown, the polarization electric field behavioras a function of cycling and electric field drive level (shown in FIG.13( b)), with the corresponding impedance characteristics for shearthickness vibration mode after fatigue measurements at different levelsare given in FIG. 13( c). For the doped crystals, the coercive field wasfound to be on the order of 6.2 kV/cm, with an internal bias field at 1kV/cm, as shown in FIG. 13( a). For an AC drive field at the level of2-4 kV/cm at 10 Hz frequency, the polarization versus electric field(PE) loops after 5000 cycles exhibited the same linear behavior as thefirst cycle, indicating the Mn-doped crystals still remain in the [111]poled condition and no domain reversal occurred. This field polarizationstability can be confirmed by the impedance-frequency characteristic ofthe shear-vibrated samples, as observed in FIG. 13( c). Furtherincreasing the AC drive field level to 5 kV/cm (near coercive field),the PE loops are larger, showing hysteretic behavior. As a consequence,the antiresonance frequency of the thickness shear vibration was foundto shift to lower frequency range, indicating degraded piezoelectricproperties. The combination of high coercive field and internal bias inmanganese modified PIN-PMN-PT crystals allowed much higher AC drivefield level compared to pure crystals.

Table I summarizes the properties of various shear modes in pure andmanganese modified relaxor-PT single crystals in accordance withexemplary embodiments in which ‘1R’, ‘1O’ and ‘1T’ are in single domainstates while the ‘2R’ configuration is in a multi domain state. Thecoercive field(s) of pure PIN-PMN-PT with R and/or O phases were foundto be on the order of 5 kV/cm, while coercive fields were 6-9 kV/cm formanganese modified crystals, with internal biases being on the order of0.6-1.8 kV/cm. The piezoelectric shear coefficient, d₁₅, andelectromechanical coupling factor, k₁₅, were found to be approximately3000 pC/N and >90%, respectively for undoped crystals, with allowable ACdrive fields at about 2 kV/cm. The manganese modified PIN-PMN-PT wasfound to possess comparable shear piezoelectric properties to theundoped counterpart, but with much higher allowable AC drive fieldlevels, being on the order of 4-5kV/cm, due to their enhanced coercivefields and developed internal biases.

For the tetragonal crystals with ‘1T’ single domain state, the coercivefields were found to be improved, being on the order of 11 kV/cm,further increasing to 11.5 kV/cm when doped with manganese, withinternal bias being 1.5 kV/cm. The allowable AC drive fields were foundto increase, being in the range of 6.5-8.5 kV/cm. The piezoelectric andelectromechanical coupling, however, were found to be about 1200 pC/Nand 0.77, respectively, for Mn doped tetragonal PIN-PMN-PT crystals. Itis interesting to note that the field stability levels (max allowable ACdrive fields divided by their respective coercive fields) are on theorder of approximately 40% for all the pure crystals, while the valuesincreased to about 60-70% for the manganese modified crystals, due tothe developed internal biases. Furthermore, it is observed withincreasing internal bias levels, the field stability levels increase.Thus, both coercive field and internal bias can play a role in fieldstability levels.

TABLE I ac field Field Poling/ Engineered Ec E_(init) d_(ij) Nrstability Stability electrode domain Crystal (kV/cm) (kV/cm) ε (pC/N)k_(ij) (Hzm) (kV/cm) Ratio 110/−110 2R (d₁₅) PMNT- 2.6 / 6000 2500 0.90500 <1 <40% Mn 111/1-10 1R (d₁₅) Pure 4.5 / 6000 3500 0.93 470 2   44%PIN PIN-Mn 6.2 1.0 8000 4100 0.94 410 4   65% 110/−110 2R (d₁₅) Pure 5.0/ 6500 2800 0.92 570 2   40% PIN PIN-Mn 7.3 1.2 4600 2200 0.91 520 5  68% 110/−110 1O (d₁₅) Pure 5.5 / 5600 3400 0.95 380 2   36% PIN PIN-Mn9.0 0.6 5800 3500 0.95 360 5.5   61% 001/100 1T (d₁₅) Pure 11.0 / 150002200 0.85 850 4-5   41% PIN PIN-Mn 11.5 1.5 8000 1200 0.77 950 6.5   57%001/110 1T (d₁₅) PIN-Mn 11.5 1.5 8000 1200 0.78 980 8.5   74%

Of particular significance is the low frequency constant (N₁₅) forcrystals with ‘1O’ engineered domain configuration, being only 360-380Hz-m, indicating the potential for low frequency transducerapplications. For tetragonal single crystals, the piezoelectric andelectromechanical properties were found to be lower than theircounterparts, with compositions in the R and/or O phases. All thetetragonal crystals exhibit higher coercive fields, being >10 kV/cm, asa result, the AC drive field increase to 4-7 kV/cm, showing improvedhigh field stability for high power applications.

The inventors have further determined that a zero or minimum response ofthe thickness shear component d₁₆ is obtained for pure and manganesedoped rhombohedral PIN-PMN-PT crystals with ‘1R’ engineered domainconfiguration by rotating around the X-axis. FIG. 14 illustrates therotation axis of the sample geometry of the PIN-PMN-PT relative to thespontaneous [111] polarization. FIG. 15 shows the measured d₁₅ and d₁₆and trend curves for ‘1R’ domain configuration yPIN-(1-y-z)PMN-zPT, withy=0.26 and z=0.29, with different rotation angles around the X-axis. Therotation angle for zero d₁₆ was found to be about 25°. The generalrotation angle around the X-axis to eliminate the transversepiezoelectric shear component for ‘1R’ domain configuration is given by:

$\gamma = {\arctan \left( \frac{d_{16}}{d_{15}} \right)}$

where the d₁₆ and d₁₅ are the values for a non-rotated [111]/(1-10)crystal.

FIG. 16, FIG. 17 and FIG. 18 show measured d₁₅ and d₁₆ strain fieldcurves for [110]/(−110) PMN-xPT and pure and doped yPIN-(1-y-z)PMN-zPT,with x=0.29, y=0.26 and z=0.29 and manganese about 1.5 mol %, crystalswith a ‘2R’ domain configuration. For the PMN-PT, the piezoelectriccoefficients d₁₅ and d₁₆ were approximately 2300 pC/N and 25 pC/N,respectively. For the pure PIN-PMN-PT the d₁₅ and d₁₆ were approximately2380 pC/N and 95 pC/N, while the d₁₅ and d₁₆ for the manganese dopedPIN-PMN-PT were approximately 850 pC/N and 5 pC/N. It will beappreciated that the value of d₁₆ is about zero in this domainconfiguration and that the somewhat larger measurements obtained can beattributed to crystal misorientation.

FIG. 19 shows the rotational angle for elimination of either the d₃₁′ ord₃₂′ transverse width extensional piezoelectric coefficient for d₃₆ faceshear [110]/(110) PMN-PT, PIN-PMN-PT and Mn-doped PIN-PMN-PT crystalswith a ‘2R’ domain configuration having the compositions as describedwith respect to FIGS. 16-18.

FIG. 20 shows the measured rotated transverse width extensionalpiezoelectric strain field curves for d₃₆ face shear [110]/(110) PMN-xPThaving a ‘2R’ domain configuration, with x=0.29. The d₃₁′ is about 780pC/N and the d₃₂′ is about −20 pC/N.

While the foregoing specification illustrates and describes exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the invention without departing from theessential scope thereof. Therefore, it is intended that the inventionnot be limited to the particular embodiment disclosed as the best modecontemplated for carrying out this invention, but that the inventionwill include all embodiments falling within the scope of the appendedclaims.

1. A piezoelectric single crystal having a composition with the formulayPb(In_(1/2)Nb_(1/2))O₃-(1-y-z) Pb(Mg_(1/3)Nb_(2/3))O₃-zPbTiO₃(“yPIN-(1-y-z)PMN-zPT”), where 0.26≦y≦0.50, 0.31<z≦0.36 and wherein thecrystal is poled along the crystallographic [110] direction, the crystalhaving an orthorhombic/monoclinic phase and ‘1O’ single domain state. 2.The crystal of claim 1, having macroscopic mm2 symmetry.
 3. The crystalof claim 1, wherein the crystal has electrodes on the (001) faces, a k₂₄of about 85%, and a shear piezoelectric coefficient d₂₄ of about 2000pC/N, the shear piezoelectric coefficient being substantiallytemperature stable in the range of about −50° C. to about T_(OT), whereT_(OT) is the orthorhombic to tetragonal phase transition temperature.4. The crystal of claim 1, wherein the crystal has electrodes on the(−110) faces, a k₁₅ of about 90%, a shear piezoelectric coefficient d₁₅of about 3000 pC/N, and has a substantially stable coercive field ofabout 5 kV/cm with an internal bias field of about 1 kV/cm such that theallowable AC field drive level is about 40% of the coercive field. 5.The crystal of claim 1, wherein the crystal is doped with between 0.2mol % to about 8 mol % of a dopant selected from the group consisting ofmanganese, iron, cobalt, nickel, aluminum, gallium, copper, potassiumsodium, fluorides, and combinations thereof.
 6. The crystal of claim 5,wherein the crystal is doped with between about 1 mol % to about 3 mol %of the dopant.
 7. The crystal of claim 5, wherein the crystal is dopedwith about 1.5 mol % manganese.
 8. The crystal of claim 5, wherein thecrystal has electrodes on the (001) faces, a k₂₄ of about 85%, and ashear piezoelectric coefficient d₂₄ of about 2000 pC/N, the shearpiezoelectric coefficient being substantially temperature stable in thetemperature range of about −50° C. to about T_(OT), where T_(OT) is theorthorhombic to tetragonal phase transition temperature.
 9. The crystalof claim 5, wherein the crystal has electrodes on the (−110) faces, ak₁₅ of about 90%, a shear piezoelectric coefficient d₁₅ of about 3000pC/N, and has a coercive field of about 7 to about 9 kV/cm with aninternal bias field of about 1 kV/cm, the allowable AC field drive levelbeing about 60-70% of the coercive field.
 10. The crystal of claim 5,wherein the crystal has electrodes on the (−110) faces and a shearpiezoelectric coefficient d₁₆ of about
 0. 11. The crystal of claim 1,wherein the crystal has electrodes on the (−110) faces and a shearpiezoelectric coefficient d₁₆ of about 0.